In quantum mechanics the delta potential is a potential well mathematically described by the Dirac delta function - a generalized function. Qualitatively, it corresponds to a potential which is zero everywhere, except at a single point, where it takes an infinite value.

Let $V(x) = −u \delta(x) - v \delta(x − a)$ where $u, v > 0$ correspond to a potential with two $\delta$ wells. Let $v > u$. If $a$ is very large, there is certainly a bound state: the particle

In the last post we had a look at the bound states of the double delta function potential V(x)= [ (x+a)+ (x a)] (1) where gives the strength of the well. In this post, we’ll look at the scat-tering states of this potential. We will use a similar approach to that …

2016年3月23日 · We study a general double Dirac delta potential to show that this is the simplest yet versatile solvable potential to introduce double wells, avoided crossings, resonances and perfect transmission ($T=1$).

We study a general double Dirac delta potential to show that this is the simplest yet still versatile solvable potential to introduce double wells, avoided crossings, resonances and perfect transmission (T = 1). Perfect transmission energies turn out to be the critical property of symmetric and anti-symmetric

Particles moving from left encounter d-function potential at x = 0: will either continue moving in +x direction (i.e., they are transmitted through the region of potential change)

2016年3月23日 · We study a general double Dirac delta potential to show that this is the simplest yet versatile solvable potential to introduce double wells, avoided crossings, resonances and perfect...

2017年10月1日 · The strength parameter for the potential is often set by considering the dissociation regime, i.e. imagining that the two nuclei are so far apart that the electron is trapped in a single $\delta$ well (and - say - setting the binding energy of the one bound state to some known value for the atom).

We can extend the case of the particle in a delta function well to the case of a particle in a double delta function well. That is, the potential is V(x)= [ (x+a)+ (x a)] (1) where gives the strength of the well. Since the potential is an even function, any solution can be expressed as a linear combination of even and odd solutions. Even solutions.

11.2 Delta Potential As an example of how the boundaries can be used to set constants, consider a -function potential well (negative), centered at the origin. For V(x) = (x), we have scattering solutions for E>0, and bound states for E<0. 11.2.1 Bound State Let’s consider the bound state rst: To the left and right of the origin, we are ...